The reason it's important is because it counts as basic mental maintenance, just as eating reasonably and exercising a bit and so on are basic bodily maintenance. You cannot achieve any goal without basic self-care.

For the solving friendly AI problem in particular: the current leader in the field has noticed his work suffers if he doesn't allow play time. You are allowed play time.

You are not a moral failure for not personally achieving an arbitrary degree of moral perfection.

You sound depressed, which would mean your hardware was even more corrupt and biased than usual. This won't help achieve a positive Singularity either. Driving yourself crazier with guilt at not being able to work for a positive Singularity won't help your effectiveness, so you need to stop doing that.

You are allowed to rest and play. You need to let yourself rest. Take a deep breath! Sleep! Go on holiday! Talk to friends you trust! See your doctor! Please do something. You sound like you are dashing your mind to pieces against the rock of the profoundly difficult, and you are not under any obligation to do such a thing, to punish yourself so.